The first International Mathematical Olympiad (IMO) was held in 1959 in Romania. It was originally intended for Eastern Bloc countries only, but since then the list has grown to over 90 of participating countries from all over the world. The site of the competition changes each year, and past locations include such diverse venues as Finland, India, Cuba, Argentina, and Bulgaria. The United States first competed in the IMO in East Germany in 1974. The United States has hosted the event in 1981 and 2001. The competition has been held every year except 1980 (due to unrest in Mongolia). When the IMO first began, each country was allowed up to eight participants. In 1982 this was scaled back to four members, but in 1983 the number was increased to six, which is where it still stands. The contestants must be no more than 20 years old and must not have any postsecondary-school education. There is no limit to how many times a person may participate in the IMO, provided the individual meets the age and schooling requirements. Even though the contestants represent their countries in the Olympiad, there are no official teams and all scoring is done on an individual basis only. Although the particular way the representatives are chosen differs from country to country, each country requires a great deal of hard work and mathematical skill from its members. The competition gives these young people a chance to display their mathematical prowess, but the actual competition comprises only two days of the two-week event. A large part of the rest of the time is spent socializing with the other students and touring the hosting country. For many who participate, the friends and memories made at the IMO outweigh the actual scores and medals. It is an experience that cannot help but shape the participants, many of whom have gone on to achieve tremendous success in their chosen fields.

What is the IMO?

Bringing math and students together is an age-old idea. Mathematical competitions have played important roles in the tradition of many countries for centuries, surely dating as far back as the Greeks competing to solve geometry problems. In the XVI century, the Italians competed to resolve cubic polynomials, the French held competitions in the XVIII century, and Hungary organized the Eotvos competitions since 1894, which is most likely the closest antecedent to the Mathematical Olympiad held today. The first Mathematical Olympiad took place in Leningrad (now San Petersburg) in 1934, organized by B.N. Delone and G.M. Frijtengolts. In 1959, Romania organized the first International Mathematical Olympiad as an eastern European regional competition with seven countries. The competition has been held every year since then, except 1980. For the first years it was restricted to the same countries, but its membership has gradually expanded to over ninety countries from five continents, and every year it is hosted by a different country. Past locations include diverse venues as Finland , India , Cuba , Argentina , Bulgaria , Greece , etc. The year 2005 marks the first time that México will be the hosting nation for the IMO. The competition will take place in the city of Mérida , Yucatán, México. México has been a member since 1988.

When the IMO first began, each country was allowed up to eight participants. In 1982, this was scaled back to four members, but in 1983 the number was increased to six, which is where it still stands. The contestants must be no more than 20 years old and must not have any post secondary-school education. There is no limit to how many times a person may participate in the IMO, provided the individual meets the age and schooling requirements. The usual size of an official delegation to an IMO is (a maximum of) six students and (a maximum of) two leaders. The student competitor writes two papers, on consecutive days, each paper consisting of three questions. Each question is worth seven marks. Only a whole number of marks are given, so there can be no half mark score.

IMO Facts

The question papers -- No later than four months before the competition, each invited country can send in up to six questions for consideration for the final competition papers. These submissions are reviewed by the host country's competitions committee, and a short list of about thirty questions is made. In recent years, there has also been a list of twelve preferred questions. The choice of the questions on the actual competition papers is made by the International Jury. The International Jury consists of the Chief Delegate (Leader) from each participating country, together with a Jury Executive of four named by the host country. Decisions are made by a simple majority vote. The International Jury meets a few days in advance of the competition in a sequestered location in order to choose the papers. The official languages of the IMO are English, French, German and Russian. Since Spanish is spoken in a large number of participating countries, it has become an unofficial 'official' language. In recent years, English has been the working language of the International Jury, with the other official languages available whenever required.

The International Jury members receive the short list of questions on arrival at the sequestered site. They have little time to review these problems before meeting to discuss which problems will be included. An honor system requires delegates to identify any suggested problems that are well known, in text books, or have been used in training programs. Some problems are eliminated as too easy or too hard. After considerable debate, the six problems are chosen, and their wording in all the official languages is agreed. The leaders of countries, whose students require other languages, then translate the questions into the required language. All papers, in all languages, are then inspected by all members of the International Jury, to ensure that all translations are appropriate.

The competition -- The students arrive a couple of days before the actual competition days, to give them time to adjust and settle into the host site. The actual competition consists of two papers, each of three questions, each paper lasting four and one half hours. Traditionally, the 1 st question is relatively easy and 6 th question is the hardest. The papers are on successive days. After they have been written, the students have a cultural and entertainment program while the papers are marked, which enables the visiting students to get a glimpse of the host country.

Marking the papers -- Because of the diversity of languages used, the leaders from each participating country mark their own students' papers in the first instance. However, they are not permitted to make any marks on the scripts. They then present their students' papers, sometimes with translations, to the team of markers (known as coordinators) appointed by the host country. Eventually, the leaders and the coordinators must agree on a mark, which is entered into the official mark book, and the book is signed by both parties. If there is a protracted disagreement, the Chief Coordinator attempts to mediate. If that does not work, the case is presented to the full International Jury for resolution by majority vote.

The results -- The International Mathematical Olympiad is an individual competition. Only individuals compete. There is no team competition. Medals are awarded to approximately the top half of the participating students. Gold, Silver and Bronze medals are awarded in the ratio of 1:2:3, with no more that 1/12 of the students getting a Gold Medal, no more that 1/4 of the students getting either a Gold or a Silver Medal and no more that 1/2 of the students getting a medal of any kind. In order to encourage more students, and to encourage students to solve complete problems, recent practice has awarded a Certificate of Honorable Mention to any student (not receiving a medal) who obtained full marks for at least one problem.

The social and cultural program -- Students will be present at an International Mathematical Olympiad for about nine days. They will typically write the competition on days four and five. While the papers are being marked (which usually takes three days), the students take part in social and cultural events organized by the host country. Examples of such events at recent IMOs have been visits to:

The Great Mayan pyramids of Chichén-Itzá, The Great Wall of China, The Winter Palace in Beijing, The Royal Palace of the Kings of Hanover, The Lower Saxony Windmill Park, The Tintidbilla Nature Reserve near Canberra, The Australian National Botanic Garden in Canberra, and The Bay of Pigs in Cuba.

Traditionally, the IMO ends with two events: a medal presentation ceremony and a final banquet/party. The medal presentation ceremonies are formal joyous events. Here is a chance for the best to receive their medals amidst public acclaim, with considerable media coverage. It is customary to have a very high ranking person from the host country as the presenter of the Gold Medal awards. The final banquet/party is a more relaxed event, with pledges of friendships across the globe.